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a) \(A=\frac{15^{16}+1}{15^{17}+1}\)và\(B=\frac{15^{15}+1}{15^{16}+1}\)
ta có \(A=\frac{15^{16}}{15^{17}}\)và\(B=\frac{15^{15}}{15^{16}}\)
ta dễ nhận thấy phần cơ số của hai phân số A và B = nhau
mà phần mũ của các lũy thừa phân số A đều lớn hơn phân số B
\(\Rightarrow\frac{15^{16}}{15^{17}}>\frac{15^{15}}{15^{16}}\)
\(\Rightarrow\frac{15^{16}+1}{15^{17}+1}>\frac{15^{15}+1}{15^{16}+1}\)
\(\Rightarrow A>B\)
\(A=\frac{15^{16}+1}{15^{17}+1}vaB=\frac{15^{15}+1}{15^{16}+1}\)
+)Ta thấy\(A=\frac{15^{16}+1}{15^{17}+1}< 1\)
\(\Rightarrow A< \frac{15^{16}+1+14}{15^{17}+1+14}=\frac{15^{16}+15}{15^{17}+15}=\frac{15.\left(15^{15}+1\right)}{15.\left(15^{15}+1\right)}=\frac{15^{15}+1}{15^{16}+1}=B\)
Vậy A<B
b)Đề sai
Chúc bạn học tốt
B=\(\dfrac{1+15^4+15^8+...+15^{96}+15^{100}}{\left(1+15^4+15^8+..+15^{96}+15^{100}\right)+\left(15^2+15^6+...+15^{98}+15^{102}\right)}\)
=\(\dfrac{1+15^4+15^8+...+15^{96}+15^{100}}{\left(1+15^4+15^8+...+15^{96}+15^{100}\right)+15^2.\left(1+15^{14}+15^8+...+15^{96}+15^{100}\right)}\)
\(\dfrac{\left(1+15^4+15^8+...+15^{96}+15^{100}\right)}{\left(1+15^4+15^8+...+15^{96}+15^{100}\right)\left(1+15^2\right)}\)
=\(\dfrac{1}{1+15^2}=\dfrac{1}{226}\)
â, -4/9(7/15+8/15)=-4/9
b,-5/4(16/25+9/25)=-5/4
,.....
dài quá mik làm ko hết
hok tốt
a: \(=\left(-\dfrac{25}{140}+\dfrac{245}{140}+\dfrac{32}{140}\right)\cdot\dfrac{-69}{20}\)
\(=\dfrac{252}{140}\cdot\dfrac{-69}{20}\)
\(=\dfrac{9}{5}\cdot\dfrac{-69}{20}=\dfrac{-621}{100}\)
b: \(=\left(6-2-\dfrac{4}{5}\right)\cdot\dfrac{25}{8}-\dfrac{8}{5}\cdot4\)
\(=\dfrac{16}{5}\cdot\dfrac{25}{8}-\dfrac{32}{5}=\dfrac{18}{5}\)
c: \(=\left(\dfrac{2}{24}+\dfrac{18}{24}+\dfrac{14}{24}\right):\dfrac{-17}{8}\)
\(=\dfrac{34}{24}\cdot\dfrac{-8}{17}=\dfrac{-1}{3}\cdot2=-\dfrac{2}{3}\)
\(E=\frac{1}{25\cdot27}+\frac{1}{27\cdot29}+...+\frac{1}{73\cdot75}\)
\(E=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(\Rightarrow E=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)
\(F=\frac{15}{90\cdot94}+\frac{15}{94\cdot98}+...+\frac{15}{146\cdot150}\)
\(F=\frac{15}{4}\cdot\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+...+\frac{1}{146}-\frac{1}{150}\right)\)
\(\Rightarrow F=\frac{15}{4}\cdot\left(\frac{1}{90}-\frac{1}{150}\right)=\frac{15}{4}\cdot\frac{1}{225}=\frac{1}{60}\)
\(G=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(G=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(G=\frac{5}{4\cdot7}+\frac{5}{7\cdot10}+\frac{5}{10\cdot13}+...+\frac{5}{25\cdot28}\)
\(G=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(\Rightarrow G=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}\cdot\frac{3}{14}=\frac{5}{14}\)
mik ko ghi lại đề nhé!
\(A=\left(\frac{18}{15}.\frac{1}{4}.3\right)+\left(-\frac{47}{60}\right).\frac{24}{47}\)
\(A=\frac{8}{5}+\left(-\frac{2}{5}\right)\)
\(A=\frac{6}{5}\)
\(B=\frac{3}{4}.\frac{28}{15}-\left(\frac{8}{15}+\frac{1}{4}\right).\frac{24}{47}-\frac{17}{13}\)
\(B=\frac{7}{5}-\frac{47}{60}.\frac{24}{47}-\frac{17}{13}\)
\(B=\frac{7}{5}-\frac{2}{5}-\frac{17}{13}\)
\(B=1-\frac{17}{13}\)
\(B=-\frac{4}{13}\)
THANKS